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# Evaluating Researcher's Claim using a Two-Tailed T-Test

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A researcher is interested in comparing the response times of two different cab companies. Companies A and B were each called at 50 randomly selected times. The calls to company A were independently made from the calls to company B. Company A had a mean response time of 8.5 minutes with a standard deviation of 1.8 minutes. Company B had a mean response time of 5.5 minutes with a standard deviation of 1.6 minutes. Use a 0.05 significance level to test the claim that the mean response time for company A differs from the mean response time for company B by doing the following:

1. State the null and alternative hypotheses symbolically and identify which represents the claim.
2. Determine whether the hypothesis test is a one-tailed test or a two-tailed test and whether or not to use a z-test or a t-test.
3. Identify the critical value(s) and identify the rejection region(s).
4. Use the appropriate test to find the appropriate test statistic. You can use technology for this question but please attach your results which must show your work.
5. Based on your test statistic and your rejection region, what is your decision?
6. Interpret your decision in context of the original claim.
7. Construct a 95% confidence interval estimate of the difference between the mean responses times for Company A and Company B. Interpret your interval in context of the original claim.

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#### Solution Preview

Hi there,

1. Null hypothesis: the mean response time for company A is same as the mean response time for company B. in other words, µA=µB
Alternative hypothesis: the mean response time for company A is different from the mean response time for company B. in other words, µA?µB.
The claim is same as the alternative hypothesis.

2. Since the sample size is bigger than 30 and ...

#### Solution Summary

The solution provides detailed explanation how to perform two tailed t test assuming equal variance.

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